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Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 1, Iss. 3 — Aug. 4, 1997
  • pp: 68–72
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Effects of two-photon absorption in saturable Bragg reflectors used in femtosecond solid state lasers

Amjad T. Obeidat, Wayne H. Knox, and Jacob B. Khurgin  »View Author Affiliations


Optics Express, Vol. 1, Issue 3, pp. 68-72 (1997)
http://dx.doi.org/10.1364/OE.1.000068


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Abstract

We analyzed the effect of two-photon absorption (TPA) on distributed Bragg reflectors and applied our results to the study of saturable Bragg reflectors in mode-locked Cr:LiSAF laser. We showed that in agreement with experimental results, TPA is greatly reduced compared to bulk materials. Hence, Bragg reflectors can be successfully used in a variety of low-loss laser components.

© Optical Society of America

The process of two-photon absorption (TPA) in semiconductors plays an important role at frequencies below the bandgap where it can dominate other absorption processes. TPA has been observed and studied in semiconductor materials of different composition and dimensionality1–3. It may be useful in such devices as optical memories4 and switches5. Developing an understanding of the macroscopic effects of such a nonlinearity is essential for the operation of a variety of optical devices. However, more often than not TPA can severely limit the performance of electro-optic devices, especially at high intensities. For example, due to TPA, the nonlinear loss of saturable absorbers and other optical switches can become prohibitively high for intra-cavity applications requiring minimal losses.

In this paper we will discuss the role of TPA in one of the more common intracavity applications of semiconductors – that of mode-locking of femtosecond Cr:LiSrAlF lasers6. It has become commonplace to use this medium to generate pulses as short as 70 fs. However, one of the shortcomings of Cr:LiSrAlF is its low gain (a few percent per pass) which makes it very sensitive to intracavity loss. Hence, extreme care must be exercised when adding components inside the cavity such as mode-lockers. This has long been the argument used against the introduction of semiconductor devices into the cavities of high peak power, ultrafast lasers. The expected effects of TPA were presumed to overwhelm the low gain of the medium. However, Semiconductor saturable absorbers have been successfully used in such lasers6 without any detrimental effects to the operation of the laser.

The saturable Bragg reflector (SBR) used in ref.(6

6 . S. Tsuda , W. H. Knox , E. A. de Souza , W. Y. Jan , and J. E. Cunningham , “ Low-loss intracavity AlAs/AlGaAs saturable Bragg reflector for femtosecond mode locking in solid-state lasers ,” Opt. Lett. 20 , 1406 ( 1995 ). [CrossRef] [PubMed]

) is simply a DBR with a single quantum well (QW) in the first quarter-wavelength layer that acts as a saturable absorbers. Using this scheme as a mode-locker and reflector combination, strong mode-locking was achieved with the average mode-locked power approximately equal to the CW power (~ 100 mW). This indicates a very low level of intracavity loss introduced by the SBR and its reflectivity is deduced to be close to 99%. Yet, if one considers the high intracavity intensity (~5 GW/cm2) focused on the SBR, then one would expect to see the effects of two-photon absorption in GaAs. Indeed, with a TPA coefficient of β = 0.05cm/MW1 and a DBR length of 3.4 μm, one would expect to observe a loss as large as 15% for a round trip through the reflector, in clear contrast to experimental results. This has led us to perform a detailed study of the effects of TPA in DBRs, taking the effect of nonreciprocity into account. To the best of our knowledge, this is the first time that TPA has been rigorously addressed in saturable DBRs.

We have modeled TPA in DBRs using the transfer matrix method7 to calculate the electric and magnetic fields in the optical waves as they propagate into the structure. The method was modified to accommodate the presence of TPA in the structure. The intensity was assumed to be constant within a given layer. This approximation is justified by the small thickness of the layers as compared to the anticipated nonlinear absorption length. The transfer matrix for one of the layers relates the total electric and magnetic fields at interface j to the fields at interface j + 1 according to

(Ej+1cBj+1)=i2(e12αide12αrd1n(e12αid+e12αrd)n(e12αid+e12αrd)e12αide12αrd)(EjcBj)
(1)

where c is the speed of light in vacuum, E and B are the electric and magnetic fields normalized by the incident electric field, E0=2ηI0, and d is the layer thickness which is a quarter wavelength. Our analysis took into account the nonreciprocity between the intensities of the counter-propagating fields. This effect occurs because the presence of one field changes the value of TPA felt by the other8. This change in TPA is nonreciprocal because of the standing wave pattern which couples the two fields. The absorption coefficients are

αi=1la(Ii+2Ir)
(2-a)
αr=1la(2Ii+Ir),
(2-b)

where {i, r} refer to the incident and reflected intensities which are normalized by the initial incident intensity. la is the nonlinear absorption length defined as la = 1/β I 0.

Fig. 1 The total optical energy density inside the DBR normalized by the incident energy density. The device structure is overlaid on the curve. The total length of the device is 3.432 μm.

Fig. 2 Reflectivity of the DBR vs. the input intensity in comparison with a similar piece of bulk GaAs in front of an ideal reflector. The operating point of 5 GW/cm2 is shown.

For comparison, we also plot the reflectivity of a more conventional saturable absorber mode-locker, consisting of a bulk cell of thickness equal to that of the DBR placed in front of an ideal reflector. It is easy to see that its reflectivity decreases drastically at intensities two orders of magnitude below that of the saturable DBR. The value of the critical intensity in the DBR where the sharp decrease in reflectivity takes place can be found to first order by considering the TPA length in the material which is defined as la = 1/βI 0. When the TPA length is equal to twice the field penetration depth, then one would expect only a few reflections to make it back to the front face bringing the reflectivity to its Fresnel value. Simple calculations show that Icr = 166 GW/cm2, i.e., well in excess of 5 GW/cm2 as confirmed by Fig. 2. Figure 3 illustrates the connection between the reflectivity and the absorption length. We estimate the penetration depth in the DBR to be 0.6μm which clearly corresponds to the region on figure 3 where the reflectivity drops.

Fig. 3 Reflectivity of the DBR as a function of the absorption length which is defined as 1/(βI 0) where I 0 is the incident intensity.

In conclusion, we have shown theoretically that in a saturable DBR the detrimental effects of TPA are dramatically reduced in comparison to a conventional saturable absorber. While it is intuitively understood that the reduction in TPA is the result of the small penetration depth in the SBR, the main result of this work is that we obtain a good numerical estimate of the maximum intensities obtainable using the SBR for passive mode-locking. This theoretical result explains the experimental data of ref. (6

6 . S. Tsuda , W. H. Knox , E. A. de Souza , W. Y. Jan , and J. E. Cunningham , “ Low-loss intracavity AlAs/AlGaAs saturable Bragg reflector for femtosecond mode locking in solid-state lasers ,” Opt. Lett. 20 , 1406 ( 1995 ). [CrossRef] [PubMed]

) and shows that even higher intracavity powers can be used in that scheme.

We acknowledge the Air Force Office of Scientific Research for supporting this work.

References

1 .

B. S. Wherrett , “ Scaling rules for multiphoton interband absorption in semiconductors ,” J. Opt. Soc. Am. B 1 , 67 – 72 ( 1984 ). [CrossRef]

2 .

J. B. Khurgin , “ Nonlinear response of the semiconductor quantum-confined structures near and below the middle of the band gap ,” J. Opt. Soc. Am. B 11 , 624 – 631 ( 1994 ). [CrossRef]

3 .

A. T. Obeidat and J. B. Khurgin , “ Excitonic enhancement of two-photon absorption in semiconductor quantum-well structures ,” J. Opt. Soc. Am. B 12 , 1222 – 1227 ( 1995 ). [CrossRef]

4 .

S. Hunter , F. Kiamilev , S. Esener , D. Parthenopoulos , and P. Rentzepis , “ Potentials of two-photon based 3D optical memories for high performance computing ,” Appl. Opt. 29 , 2058 – 2066 ( 1990 ). [CrossRef] [PubMed]

5 .

A. Villeneuve , C. C. Yang , P. G. Wigley , G. I. Stegeman , and J. S. Aitchison , “ Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap ,” Appl. Phys. Lett. 62 , 147 – 149 ( 1992 ). [CrossRef]

6 .

S. Tsuda , W. H. Knox , E. A. de Souza , W. Y. Jan , and J. E. Cunningham , “ Low-loss intracavity AlAs/AlGaAs saturable Bragg reflector for femtosecond mode locking in solid-state lasers ,” Opt. Lett. 20 , 1406 ( 1995 ). [CrossRef] [PubMed]

7 .

F. Pedrotti and L. Pedrotti , Introduction To Optics , ( Printice Hall, New Jersey , 1993 ), p. 391 .

8 .

A. Kaplan , “ Light-induced nonreciprocity, field invariants, and nonlinear eigenpolarizations ,” Opt. Lett. 8 , 560 ( 1983 ). [CrossRef] [PubMed]

OCIS Codes
(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

ToC Category:
Research Papers

History
Original Manuscript: June 20, 1997
Revised Manuscript: June 20, 1997
Published: August 4, 1997

Citation
Amjad Obeidat, Jacob Khurgin, and Wayne Knox, "Effects of two-photon absorption in saturable Bragg reflectors used in femtosecond solid state lasers," Opt. Express 1, 68-72 (1997)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-1-3-68


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References

  1. B. S. Wherrett, "Scaling rules for multiphoton interband absorption in semiconductors," J. Opt. Soc. Am. B 1, 67-72 (1984). [CrossRef]
  2. J. B. Khurgin, "Nonlinear response of the semiconductor quantum-confined structures near and below the middle of the band gap," J. Opt. Soc. Am. B 11, 624-631 (1994). [CrossRef]
  3. A. T. Obeidat, J. B. Khurgin, "Excitonic enhancement of two-photon absorption in semiconductor quantum-well structures," J. Opt. Soc. Am. B 12, 1222-1227 (1995). [CrossRef]
  4. S. Hunter, F. Kiamilev, S. Esener, D. Parthenopoulos, and P. Rentzepis, "Potentials of two-photon based 3D optical memories for high performance computing," Appl. Opt. 29, 2058-2066 (1990). [CrossRef] [PubMed]
  5. A. Villeneuve, C. C. Yang, P. G. Wigley, G. I. Stegeman, J. S. Aitchison, "Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap," Appl. Phys. Lett. 62, 147-149 (1992). [CrossRef]
  6. S. Tsuda, W. H. Knox, E. A. de Souza, W. Y. Jan, J. E. Cunningham, "Low-loss intracavity AlAs/AlGaAs saturable Bragg reflector for femtosecond mode locking in solid-state lasers," Opt. Lett. 20, 1406 (1995). [CrossRef] [PubMed]
  7. F. Pedrotti, L. Pedrotti, Introduction To Optics, (Printice HAll, New Jersey, 1993), p. 391.
  8. A. Kaplan, "Light-induced nonreciprocity, field invariants, and nonlinear eigenpolarizations," Opt. Lett. 8, 560 (1983). [CrossRef] [PubMed]

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